Distributionally Robust Optimization-based Ordering Decision And Contract Design In The Presence Of Stochastic Yield,demand And Price

In the context of supply chain globalization and COVID-19 pandemic,various uncertainties(e.g.,yield,demand,price)pose new challenges to supply chain decision-making(e.g.,ordering,cooperation).To improve the robustness and stability of supply chain,how to investigate ordering decision and contract design with the concern of stochastic yield,demand,and price is the critical challenge and opportunity.In terms of the above-mentioned issue,stochastic programming framework is very popular in the literature.This approach assumes that the probability distribution of uncertain or stochastic parameters are known.However,it is difficult to obtain the true probability distribution of the uncertain or stochastic parameters in supply chain management practice.Decision entities only have an access to partial distribution information.In this case,there exists a set of distributions satisfying the partial distribution information,called"ambiguity set".Since it is challenging for decision entities to identify the true distribution from the ambiguity set,it will perform poorly under the true distribution if the optimal decision is achieved based on a wrong probability distribution.Accordingly,this dissertation introduces a first-order and second-order moment based distributionally robust optimization method to capture the relationship among multiple uncertainties.It is further applied to study contract design with the concern of multiple uncertainties under maximin criterion,and newsvendor ordering decision problem in the presence of multiple uncertainties under Hurwicz criterion.Firstly,for revenue sharing contract design problem considering stochastic demand and yield,a moment based distributionally robust optimization method is used to construct a twostage Stackelberg-game model for manufacturers and retailers.Then,supply chain performance is compared under decentralized and centralized situation,thus proposing a full-subsidyrevenue-sharing contract.In addition,the benchmark model is further extended to relevant issues with price endogeneity and information asymmetry.Results indicate that the pure revenue sharing contract can’t coordinate the supply chain.The improved revenue sharing contract can achieve not only supply chain coordination,but Pareto improvement of both contract parties’profits under a certain condition.Secondly,in terms of protection price contract design issue considering stochastic yield,demand,and market spot price,the equilibrium solutions and performance of producers and distributors or retailers in a two-stage decision are obtained by Stackelberg-game theory and a moment based distributionally robust optimization approach.The protection price contract is respectively compared by fixed procurement price contract and market spot price contract,thus analyzing the intrinsic mechanism of the protection price contract.By analyzing the supply chain performance in the decentralized and centralized situation,the impacts of uncertain yield and demand on game players’ equilibrium strategies and performance,and the maximum willingness to pay to obtain full information about the true distribution are investigated.Results demonstrate that when the market condition is not so good,the protection price contract is equivalent to the fixed procurement price contract.At this time,maximizing both the contract parties’ profits are achieved.However,when the market condition is good,the protection price contract is equivalent to the market spot price contract.In this case,in order to prevent the opportunistic behavior of manufacturers(e.g.,farmers)and maintain stable supply,distributors or retailers(e.g.,agribusiness firm)have to pay for it.Additionally,it is found that it can’t coordinate the supply chain when the protection price contract is equivalent to the fixed procurement price contract.However,the supply chain coordination can be achieved under a certain condition when the protection price contract is equivalent to the market spot price contract.Thirdly,regarding Hurwicz criterion-based ordering decision problem in the inclusion of stochastic yield,demand,and sale price,the closed-form expression of the expected profits of demand entities(e.g.,retailers)under the maximin and maximax criterion are obtained by a moment based distributionally robust optimization framework,linear conic and convex optimization theory.Then,the optimal closed-form solution of newsvendor ordering decision under the Hurwicz criterion is further derived.In addition,the impacts of the attitude of decision entities(e.g.,retailers)towards the distribution ambiguity on ordering decision are observed by comparing with the results under different criteria and also the out-of-sample performance under different decision criterion are examined.Results indicate that the optimal closed-form solutions of Hurwicz criterion-based ordering decision can be divided into two cases according to the profit margin of the products.Each case is a piecewise function with respect to the optimistic coefficient.In detail,when the profit margin of the products is relatively low,if the optimistic coefficient is relatively small,the optimal ordering quantity increases with an ascending the coefficient of optimism.It gradually increases from the order quantity under the maximin criterion to that under the maximax criterion.Otherwise,the optimal order quantity remains the same and is equal to that under the maximax criterion.When the profit margin of the products is relatively high,if the coefficient of optimism is relatively small,the optimal order quantity decreases with a descending the coefficient of optimism.It gradually decreases from the order quantity under the maximin criterion to that under the maximax criterion.Otherwise,it also remains the same and equals to the order quantity under the maximax criterion.This suggests that the ordering behavior of decision entities(e.g.,retailers)depends on not only their attitude towards the distribution ambiguity but the profit margin of the products.